Communication systems employ forward error correction in order to correct errors caused by noise generated in transport channels. For example, a communication system typically uses a turbo code for the forward error correction. At the transmitter side, turbo encoder introduces redundancy bits based on information bits. The encoded bits at the output of turbo encoder are then modulated and transmitted to the receiver. At the receiver end, the receiver demodulates the received signal and produce received encoded bits to the turbo decoder. Turbo decoder decodes the received encoded bits to recover the information bits.
To maximize the advantage of the coding gain obtained by the iterative decoding process in the turbo decoder, rather than determining immediately whether received encoded bits are zero or one, the communication receiver assigns each bit of value on a multi level scale representative of the probability that the bit is 1. A common scale, referred to as Log-Likelihood Ratio (LLR) probabilities, represents each bit in an integer in some range, for example −32 to 31. The value of 31 signifies that the transmitted bit was 0 with a very high probability, and a value of −32 signifies that the transmitted bit was 1 with a very high probability. A value of 0 indicates that the logical bit value is indeterminate.
The turbo decoder in a communication receiver uses the LLR to determine whether a given information bit were transmitted given a particular received encoded bits. However, the computation of the LLR probabilities is a time-consuming and processing-intensive calculation. By way of explanation, in a transmitter of a communication system, each N encoded bits are mapped to one symbol (2 dimensional symbol with I and Q components). The symbol is transmitted over a channel to reach a receiver. The received symbol is attenuated and corrupted by noise. The task of the receiver's demodulator is to recover the N encoded bits from that noisy received symbol. To utilize the coding gain of the turbo decoder, N soft bits (or LLR) are generated.
Usually, the log likelihood is used to approximate the soft bit. The log likelihood L(bi) for i-th bit (i=0, 1, . . . , N−1) is calculated as:
                              L          ⁡                      (                          b              i                        )                          =                ⁢                  ln          ⁢                                    P              ⁡                              (                                                      b                    i                                    =                                      0                    ❘                    y                                                  )                                                    P              ⁡                              (                                                      b                    i                                    =                                      1                    ❘                    y                                                  )                                                                            =                ⁢                  ln          ⁢                                                    ∑                                                      z                    ❘                                          b                      i                                                        =                  0                                            ⁢                              P                ⁡                                  (                                      z                    ❘                    y                                    )                                                                                    ∑                                                      z                    ❘                                          b                      i                                                        =                  1                                            ⁢                              P                ⁡                                  (                                      z                    ❘                    y                                    )                                                                                            ≈                ⁢                              1                          2              ⁢                              σ                2                                              ⁢                      (                                                            min                                                            z                      ❘                                              b                        i                                                              =                    1                                                  ⁢                                                                                                y                      -                      z                                                                            2                                            -                                                min                                                            z                      ❘                                              b                        i                                                              =                    0                                                  ⁢                                                                                                y                      -                      z                                                                            2                                                      )                              where y is the received symbol, z is a symbol in the reference constellation, and σ2 is noise variance. From this formula, it can be seen that significant computational complexity is involved in the estimation of σ2, the estimation of the reference constellation (estimation of average amplitude of the desired signal), the calculation of the distances and min searches and the division to derive L(bi)
In order to simplify the log likelihood computation, a simplified method is proposed in International Patent Application No WO 01/67617 for generating the soft decisions. A particular example described in that document is the demodulation of a 16 Quadrature Amplitude Modulation (QAM) signal in a spread spectrum communication system. A 16 QAM constellation is shown in FIG. 1, where each of the 16 symbols in the constellation corresponds to 4 encoded bits. FIG. 2 highlights the relationship between the encoded bits and the location of each symbol. For example, if b0=1 and b1=0, the symbol has negative I and positive Q component. Based on similar observations for b1 and b3, soft bits L(bi) can be generated as follows:L(b0)=yI,L(b1)=yQ,L(b2)=Sth−abs(yI),L(b3)=Sth−abs(yQ)However, a complex circuit must be used in the arrangement described in the above-mentioned document for calculation of Sthi, which involves:
(i) calculation of interference power and calculation of desired signal power for each multipath based on pilot signal, and
(ii) mapping signal and interference power to C/I for each path, and summing to get total C/I, which is then used as an estimate of the threshold Sthi 
Accordingly, there currently remains a need to compute log-likelihood ratios for use by a turbo decoder in a computationally simple manner.